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Abstract

Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order to fill this gap, we present a framework for describing the emergence of recurrent synchronization in complex networks with adaptive interactions. This phenomenon is manifested at the macroscopic level by temporal episodes of coherent and incoherent dynamics that alternate recurrently. At the same time, the dynamics of the individual nodes do not change qualitatively. We identify asymmetric adaptation rules and temporal separation between the adaptation and the dynamics of individual nodes as key features for the emergence of recurrent synchronization. Our results suggest that asymmetric adaptation might be a fundamental ingredient for recurrent synchronization phenomena as seen in pattern generators, e.g., in neuronal systems. We describe a phenomenon of recurrent synchronization in complex dynamical networks with asymmetric adaptivity. The recurrent synchronization describes a generic mechanism of a repeating abrupt loss and gain of synchronization in complex dynamical networks. From an applied perspective, our results show how adaptation mechanisms can play a fundamental role for pattern generators, e.g., in neuronal systems. Methodologically, we present a framework for studying complex temporal patterns in adaptive dynamical networks. This mechanisms might be relevant for the understanding of the pathophysiology of Parkinsonian resting tremor and other impaired central pattern generators.